Apple'sCurvedBatteryResearchCouldPointToThinneriPhones,iWatch

Two new patent applications (1, 2) submitted to the U.S. Patent and Trademark Office reveal that Apple has been researching interesting and unorthodox battery designs, in which the battery itself curves or tapers at one end. It is anticipated that such batteries, if developed and implemented, would allow the company to produce a thinner line of iDevices, including Apple's highly anticipated "iWatch" product.
As you can see, a curve at the end of the proposed battery would allow for a more efficient use of space inside the electronic device, since the battery itself could occupy the contours at the edge of the product. Apple Insider reproduces the following text from the filing's summary, in which such functionality is outlined clearly:

In some embodiments, the curve is formed to facilitate efficient use of space inside a portable electronic device. For example, the curve may be formed at one or more ends of the battery cell to allow the battery cell to occupy a curved and/or rounded space within the enclosure of a laptop computer, tablet computer, mobile phone, personal digital assistant (PDA), digital camera, portable media player, and/or other type of battery-powered electronic device.